论文标题
统计学习和逆问题：一种随机梯度方法
Statistical Learning and Inverse Problems: A Stochastic Gradient Approach
论文作者
论文摘要
逆问题在科学和工程学中至关重要。在本文中，我们考虑了统计逆问题（SIP）的设置，并演示如何在线性SIP设置中使用随机梯度下降（SGD）算法。我们为多余风险提供一致性和有限样本范围。我们还提出了对SGD算法的修改，我们利用机器学习方法来平滑随机梯度并改善经验性能。如今，我们在引起极大兴趣的环境中举例说明了算法：功能线性回归模型。在这种情况下，我们考虑一个合成数据示例和具有真实数据分类问题的示例。
Inverse problems are paramount in Science and Engineering. In this paper, we consider the setup of Statistical Inverse Problem (SIP) and demonstrate how Stochastic Gradient Descent (SGD) algorithms can be used in the linear SIP setting. We provide consistency and finite sample bounds for the excess risk. We also propose a modification for the SGD algorithm where we leverage machine learning methods to smooth the stochastic gradients and improve empirical performance. We exemplify the algorithm in a setting of great interest nowadays: the Functional Linear Regression model. In this case we consider a synthetic data example and examples with a real data classification problem.
